The defending Stanley Cup champions rallied from a 3-1 deficit, getting five saves from Tim Thomas in as many attempts by the Sabres during the shootout.
Thomas was coming off back-to-back shutouts, but allowed three goals in the game's first 31 minutes. He finished with 31 saves.
Brad Marchand brought the Bruins within one with 4 minutes left in the middle period and Zdeno Chara tied it on the power play 3:35 into the third.
Jhonas Enroth made 36 saves for Buffalo. Pouliot beat Enroth in the shootout by putting a shot just under the crossbar.
Boston's surge has followed a slow start in which the Bruins won just three times in their first 10 games.
Celebrity Families of 2014 [PHOTOS]